Aiming at a comprehensive and concise tutorial survey, recap of variational inference and reinforcement learning with Probabilistic Graphical Models are given with detailed derivations. Reviews and comparisons on recent advances in deep reinforcement learning are made from various aspects. We offer detailed derivations to a taxonomy of Probabilistic Graphical Model and Variational Inference methods in deep reinforcement learning, which serves as a complementary material on top of the original contributions.
A Bayesian network is a graphical model that encodes probabilistic relationships among variables of interest. When used in conjunction with statistical techniques, the graphical model has several advantages for data analysis. One, because the model encodes dependencies among all variables, it readily handles situations where some data entries are missing. Two, a Bayesian network can be used to learn causal relationships, and hence can be used to gain understanding about a problem domain and to predict the consequences of intervention. Three, because the model has both a causal and probabilisti…
The framework of reinforcement learning or optimal control provides a mathematical formalization of intelligent decision making that is powerful and broadly applicable. While the general form of the reinforcement learning problem enables effective reasoning about uncertainty, the connection between reinforcement learning and inference in probabilistic models is not immediately obvious. However, such a connection has considerable value when it comes to algorithm design: formalizing a problem as probabilistic inference in principle allows us to bring to bear a wide array of approximate inference…
DeepMind（深度思维）；Massachusetts Institute of Technology（麻省理工学院）
PGMax is an open-source Python package for (a) easily specifying discrete Probabilistic Graphical Models (PGMs) as factor graphs; and (b) automatically running efficient and scalable loopy belief propagation (LBP) in JAX. PGMax supports general factor graphs with tractable factors, and leverages modern accelerators like GPUs for inference. Compared with existing alternatives, PGMax obtains higher-quality inference results with up to three orders-of-magnitude inference time speedups. PGMax additionally interacts seamlessly with the rapidly growing JAX ecosystem, opening up new research possibil…
University of Massachusetts（马萨诸塞大学）；Microsoft Research（微软研究院）
Instead of requiring a domain expert to specify the probabilistic dependencies of the data, in this work we present an approach that uses the relational DB schema to automatically construct a Bayesian graphical model for a database. This resulting model contains customized distributions for columns, latent variables that cluster the data, and factors that reflect and represent the foreign key links. Experiments demonstrate the accuracy of the model and the scalability of inference on synthetic and real-world data.
Probabilistic graphical models combine the graph theory and probability theory to give a multivariate statistical modeling. They provide a unified description of uncertainty using probability and complexity using the graphical model. Especially, graphical models provide the following several useful properties: - Graphical models provide a simple and intuitive interpretation of the structures of probabilistic models. On the other hand, they can be used to design and motivate new models. - Graphical models provide additional insights into the properties of the model, including the conditional in…
Technical University of Munich（慕尼黑工业大学）；Bosch Center for Artificial intelligence（博世人工智能中心）
Probabilistic graphical models are traditionally known for their successes in generative modeling. In this work, we advocate layered graphical models (LGMs) for probabilistic discriminative learning. To this end, we design LGMs in close analogy to neural networks (NNs), that is, they have deep hierarchical structures and convolutional or local connections between layers. Equipped with tensorized truncated variational inference, our LGMs can be efficiently trained via backpropagation on mainstream deep learning frameworks such as PyTorch. To deal with continuous valued inputs, we use a simple y…
Hanyang University（汉阳大学）；Baylor College of Medicine（贝勒医学院）；Rice University（莱斯大学）；University of Toronto（多伦多大学）；Uber ATG Toronto（优步先进技术集团多伦多分部）；Vector Institute（向量研究所）；Canadian Institute for Advanced Research（加拿大高等研究院）
A fundamental computation for statistical inference and accurate decision-making is to compute the marginal probabilities or most probable states of task-relevant variables. Probabilistic graphical models can efficiently represent the structure of such complex data, but performing these inferences is generally difficult. Message-passing algorithms, such as belief propagation, are a natural way to disseminate evidence amongst correlated variables while exploiting the graph structure, but these algorithms can struggle when the conditional dependency graphs contain loops. Here we use Graph Neural…
Integration of reinforcement learning and imitation learning is an important problem that has been studied for a long time in the field of intelligent robotics. Reinforcement learning optimizes policies to maximize the cumulative reward, whereas imitation learning attempts to extract general knowledge about the trajectories demonstrated by experts, i.e., demonstrators. Because each of them has their own drawbacks, methods combining them and compensating for each set of drawbacks have been explored thus far. However, many of the methods are heuristic and do not have a solid theoretical basis. I…
This paper presents foundational theoretical results on distributed parameter estimation for undirected probabilistic graphical models. It introduces a general condition on composite likelihood decompositions of these models which guarantees the global consistency of distributed estimators, provided the local estimators are consistent.
School of Human Sciences & Technology, IE University（IE大学人文科学与技术学院）
We show how to apply Sobol's method of global sensitivity analysis to measure the influence exerted by a set of nodes' evidence on a quantity of interest expressed by a Bayesian network. Our method exploits the network structure so as to transform the problem of Sobol index estimation into that of marginalization inference. This way, we can efficiently compute indices for networks where brute-force or Monte Carlo based estimators for variance-based sensitivity analysis would require millions of costly samples. Moreover, our method gives exact results when exact inference is used, and also supp…
We show that the log-likelihood of several probabilistic graphical models is Lipschitz continuous with respect to the lp-norm of the parameters. We discuss several implications of Lipschitz parametrization. We present an upper bound of the Kullback-Leibler divergence that allows understanding methods that penalize the lp-norm of differences of parameters as the minimization of that upper bound. The expected log-likelihood is lower bounded by the negative lp-norm, which allows understanding the generalization ability of probabilistic models. The exponential of the negative lp-norm is involved i…
Federal University of Technology - Paraná (UTFPR)（联邦理工大学-巴拉那州（UTFPR））；The University of Adelaide（阿德莱德大学）；Aalborg University（奥尔堡大学）
The Bayesian Optimisation Algorithm (BOA) is an Estimation of Distribution Algorithm (EDA) that uses a Bayesian network as probabilistic graphical model (PGM). Determining the optimal Bayesian network structure given a solution sample is an NP-hard problem. This step should be completed at each iteration of BOA, resulting in a very time-consuming process. For this reason most implementations use greedy estimation algorithms such as K2. However, we show in this paper that significant changes in PGM structure do not occur so frequently, and can be particularly sparse at the end of evolution. A s…
Mila（米拉研究所）；Université de Montréal（蒙特利尔大学）；Princeton University（普林斯顿大学）；X - The Moonshot Factory（X——登月工厂）
We investigate a correspondence between two formalisms for discrete probabilistic modeling: probabilistic graphical models (PGMs) and tensor networks (TNs), a powerful modeling framework for simulating complex quantum systems. The graphical calculus of PGMs and TNs exhibits many similarities, with discrete undirected graphical models (UGMs) being a special case of TNs. However, more general probabilistic TN models such as Born machines (BMs) employ complex-valued hidden states to produce novel forms of correlation among the probabilities. While representing a new modeling resource for capturin…
Reciprocal processes are acausal generalizations of Markov processes introduced by Bernstein in 1932. In the literature, a significant amount of attention has been focused on developing dynamical models for reciprocal processes. In this paper, we provide a probabilistic graphical model for reciprocal processes. This leads to a principled solution of the smoothing problem via message passing algorithms. For the finite state space case, convergence analysis is revisited via the Hilbert metric.
Two of the most popular modelling paradigms in computer vision are feed-forward neural networks (FFNs) and probabilistic graphical models (GMs). Various connections between the two have been studied in recent works, such as e.g. expressing mean-field based inference in a GM as an FFN. This paper establishes a new connection between FFNs and GMs. Our key observation is that any FFN implements a certain approximation of a corresponding Bayesian network (BN). We characterize various benefits of having this connection. In particular, it results in a new learning algorithm for BNs. We validate the …
Princeton University（普林斯顿大学）；Lewis-Sigler Institute for Integrative Genomics（刘易斯-西格勒综合基因组学研究所）
Probabilistic graphical models (PGMs) have become a popular tool for computational analysis of biological data in a variety of domains. But, what exactly are they and how do they work? How can we use PGMs to discover patterns that are biologically relevant? And to what extent can PGMs help us formulate new hypotheses that are testable at the bench? This note sketches out some answers and illustrates the main ideas behind the statistical approach to biological pattern discovery.
We present an algorithm to identify sparse dependence structure in continuous and non-Gaussian probability distributions, given a corresponding set of data. The conditional independence structure of an arbitrary distribution can be represented as an undirected graph (or Markov random field), but most algorithms for learning this structure are restricted to the discrete or Gaussian cases. Our new approach allows for more realistic and accurate descriptions of the distribution in question, and in turn better estimates of its sparse Markov structure. Sparsity in the graph is of interest as it can…
École Normale Supérieure（巴黎高等师范学院）；Université Paris Diderot（巴黎狄德罗大学）；Tokyo Institute of Technology（东京工业大学）；Massachusetts Institute of Technology（麻省理工学院）
These are notes from the lecture of Devavrat Shah given at the autumn school "Statistical Physics, Optimization, Inference, and Message-Passing Algorithms", that took place in Les Houches, France from Monday September 30th, 2013, till Friday October 11th, 2013. The school was organized by Florent Krzakala from UPMC & ENS Paris, Federico Ricci-Tersenghi from La Sapienza Roma, Lenka Zdeborova from CEA Saclay & CNRS, and Riccardo Zecchina from Politecnico Torino. This lecture of Devavrat Shah (MIT) covers the basics of inference and learning. It explains how inference problems are represented wit…
CIRAD（法国农业研究与国际合作组织）；Inria（法国国家信息与自动化研究所）；Univ. Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；Laboratoire Jean Kuntzmann（让·库茨曼实验室）
Multivariate count data are defined as the number of items of different categories issued from sampling within a population, which individuals are grouped into categories. The analysis of multivariate count data is a recurrent and crucial issue in numerous modelling problems, particularly in the fields of biology and ecology (where the data can represent, for example, children counts associated with multitype branching processes), sociology and econometrics. We focus on I) Identifying categories that appear simultaneously, or on the contrary that are mutually exclusive. This is achieved by ide…
Norwegian University of Science and Technology（挪威科技大学）；Aalborg University（奥尔堡大学）
In this paper, we discuss software design issues related to the development of parallel computational intelligence algorithms on multi-core CPUs, using the new Java 8 functional programming features. In particular, we focus on probabilistic graphical models (PGMs) and present the parallelisation of a collection of algorithms that deal with inference and learning of PGMs from data. Namely, maximum likelihood estimation, importance sampling, and greedy search for solving combinatorial optimisation problems. Through these concrete examples, we tackle the problem of defining efficient data structu…
Probabilistic graphical models are a powerful concept for modeling high-dimensional distributions. Besides modeling distributions, probabilistic graphical models also provide an elegant framework for performing statistical inference; because of the high-dimensional nature, however, one must often use approximate methods for this purpose. Belief propagation performs approximate inference, is efficient, and looks back on a long success-story. Yet, in most cases, belief propagation lacks any performance and convergence guarantees. Many realistic problems are presented by graphical models with loo…
A graphical model encodes conditional independence relations via the Markov properties. For an undirected graph these conditional independence relations can be represented by a simple polytope known as the graph associahedron, which can be constructed as a Minkowski sum of standard simplices. There is an analogous polytope for conditional independence relations coming from a regular Gaussian model, and it can be defined using multiinformation or relative entropy. For directed acyclic graphical models and also for mixed graphical models containing undirected, directed and bidirected edges, we g…
Max-Planck-Institut für Quantenoptik（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心（MCQST））
Tensor networks have found a wide use in a variety of applications in physics and computer science, recently leading to both theoretical insights as well as practical algorithms in machine learning. In this work we explore the connection between tensor networks and probabilistic graphical models, and show that it motivates the definition of generalized tensor networks where information from a tensor can be copied and reused in other parts of the network. We discuss the relationship between generalized tensor network architectures used in quantum physics, such as string-bond states, and archite…
A.I. SQUARE CONNECT；LAMSADE；Paris Dauphine University（巴黎多芬大学）；Université Paris Dauphine（巴黎多芬大学）
In this paper, we revisit the Kalman filter theory. After giving the intuition on a simplified financial markets example, we revisit the maths underlying it. We then show that Kalman filter can be presented in a very different fashion using graphical models. This enables us to establish the connection between Kalman filter and Hidden Markov Models. We then look at their application in financial markets and provide various intuitions in terms of their applicability for complex systems such as financial markets. Although this paper has been written more like a self contained work connecting Kalm…
In this tutorial, I will discuss the details about how Probabilistic Latent Semantic Analysis (PLSA) is formalized and how different learning algorithms are proposed to learn the model.
Probabilistic Graphical Model using Graph Neural Networks for Bayesian Inversion of Discrete Structural Component States
Key Lab of Smart Prevention and Mitigation of Civil Engineering Disasters of the Ministry of Industry and Information Technology（工信部智能防灾减灾重点实验室）；Harbin Institute of Technology（哈尔滨工业大学）；Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education, School of Civil Engineering, Harbin, Institute of Technology（教育部结构动力行为与控制重点实验室，土木工程学院）；The Institute of Statistical Mathematics, Research Organization of Information and Systems（统计数学研究所，信息与系统研究机构）；The Graduate University for Advanced Studies, SOKENDAI（高等研究大学，SOKENDAI）；Division of Engineering and Applied Science, California Institute of Technology（工程与应用科学系，加州理工学院）
Probabilistic graphical models (PGMs) provide a compact representation of knowledge that can be queried in a flexible way: after learning the parameters of a graphical model once, new probabilistic queries can be answered at test time without retraining. However, when using undirected PGMS with hidden variables, two sources of error typically compound in all but the simplest models (a) learning error (both computing the partition function and integrating out the hidden variables is intractable); and (b) prediction error (exact inference is also intractable). Here we introduce query training (Q…
University of Massachusetts, Amherst（马萨诸塞大学阿默斯特分校）；Johns Hopkins University（约翰斯·霍普金斯大学）
Probabilistic graphical models are a fundamental tool in probabilistic modeling, machine learning and artificial intelligence. They allow us to integrate in a natural way expert knowledge, physical modeling, heterogeneous and correlated data and quantities of interest. For exactly this reason, multiple sources of model uncertainty are inherent within the modular structure of the graphical model. In this paper we develop information-theoretic, robust uncertainty quantification methods and non-parametric stress tests for directed graphical models to assess the effect and the propagation through …
How do Probabilistic Graphical Models and Graph Neural Networks Look at Network Data?
Department of Physics and Astronomy, University of Bologna（博洛尼亚大学物理与天文学系）；Max Planck Institute for Intelligent Systems, Cyber Valley（智能系统马克斯·普朗克研究所，Cyber Valley）；Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology（代尔夫特理工大学电子工程、数学与计算机科学学院）
Max-Planck-Institut für Informatik（马克斯·普朗克信息学研究所）；Universität des Saarlandes（萨尔大学）
One of the major hurdles preventing the full exploitation of information from online communities is the widespread concern regarding the quality and credibility of user-contributed content. Prior works in this domain operate on a static snapshot of the community, making strong assumptions about the structure of the data (e.g., relational tables), or consider only shallow features for text classification. To address the above limitations, we propose probabilistic graphical models that can leverage the joint interplay between multiple factors in online communities --- like user interactions, com…
The University of Tokyo（东京大学）；Princeton University（普林斯顿大学）；Facebook Reality Labs（Facebook现实实验室）；Columbia University（哥伦比亚大学）；Intel Corporation（英特尔公司）
With the wide adoption of functional magnetic resonance imaging (fMRI) by cognitive neuroscience researchers, large volumes of brain imaging data have been accumulated in recent years. Aggregating these data to derive scientific insights often faces the challenge that fMRI data are high-dimensional, heterogeneous across people, and noisy. These challenges demand the development of computational tools that are tailored both for the neuroscience questions and for the properties of the data. We review a few recently developed algorithms in various domains of fMRI research: fMRI in naturalistic ta…
A D-Wave quantum annealer (QA) having a 2048 qubit lattice, with no missing qubits and couplings, allowed embedding of a complete graph of a Restricted Boltzmann Machine (RBM). A handwritten digit OptDigits data set having 8x7 pixels of visible units was used to train the RBM using a classical Contrastive Divergence. Embedding of the classically-trained RBM into the D-Wave lattice was used to demonstrate that the QA offers a high-efficiency alternative to the classical Markov Chain Monte Carlo (MCMC) for reconstructing missing labels of the test images as well as a generative model. At any tra…
In the context of dynamic emission tomography, the conventional processing pipeline consists of independent image reconstruction of single time frames, followed by the application of a suitable kinetic model to time activity curves (TACs) at the voxel or region-of-interest level. The relatively new field of 4D PET direct reconstruction, by contrast, seeks to move beyond this scheme and incorporate information from multiple time frames within the reconstruction task. Existing 4D direct models are based on a deterministic description of voxels' TACs, captured by the chosen kinetic model, conside…
Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, School of Artificial Intelligence, Beihang University（北京未来区块链与隐私计算先进创新中心，人工智能学院，北京航空航天大学）；Tsinghua University（清华大学）
针对准则奖励中因忽略准则间依赖关系导致的虚假信用传播问题，提出概率图框架Graphical Event Aggregation for Rubric rewards (GEAR)，通过建模潜在伯努利事件和软抑制传播实现依赖感知的奖励聚合，在多个基准上提升性能并减少信用泄漏。
With the arrival of the R packages nlme and lme4, linear mixed models (LMMs) have come to be widely used in experimentally-driven areas like psychology, linguistics, and cognitive science. This tutorial provides a practical introduction to fitting LMMs in a Bayesian framework using the probabilistic programming language Stan. We choose Stan (rather than WinBUGS or JAGS) because it provides an elegant and scalable framework for fitting models in most of the standard applications of LMMs. We ease the reader into fitting increasingly complex LMMs, first using a two-condition repeated measures sel…
In the Bayesian paradigm for presenting forensic evidence to court, it is recommended that the weight of the evidence be summarized as a likelihood ratio (LR) between two opposing hypotheses of how the evidence could have been produced. Such LRs are necessarily based on probabilistic models, the parameters of which may be uncertain. It has been suggested by some authors that the value of the LR, being a function of the model parameters should therefore also be considered uncertain and that this uncertainty should be communicated to the court. In this tutorial, we consider a simple example of a…
We present a novel approach to detecting and utilizing symmetries in probabilistic graphical models with two main contributions. First, we present a scalable approach to computing generating sets of permutation groups representing the symmetries of graphical models. Second, we introduce orbital Markov chains, a novel family of Markov chains leveraging model symmetries to reduce mixing times. We establish an insightful connection between model symmetries and rapid mixing of orbital Markov chains. Thus, we present the first lifted MCMC algorithm for probabilistic graphical models. Both analytica…
We incorporate discrete and continuous time Markov processes as building blocks into probabilistic graphical models with latent and observed variables. We introduce the automatic Backward Filtering Forward Guiding (BFFG) paradigm (Mider et al., 2021) for programmable inference on latent states and model parameters. Our starting point is a generative model, a forward description of the probabilistic process dynamics. We backpropagate the information provided by observations through the model to transform the generative (forward) model into a pre-conditional model guided by the data. It approxim…
University of Massachusetts, Amherst（马萨诸塞大学阿默斯特分校）
We present an information-based uncertainty quantification method for general Markov Random Fields. Markov Random Fields (MRF) are structured, probabilistic graphical models over undirected graphs, and provide a fundamental unifying modeling tool for statistical mechanics, probabilistic machine learning, and artificial intelligence. Typically MRFs are complex and high-dimensional with nodes and edges (connections) built in a modular fashion from simpler, low-dimensional probabilistic models and their local connections; in turn, this modularity allows to incorporate available data to MRFs and e…
An inductive probabilistic classification rule must generally obey the principles of Bayesian predictive inference, such that all observed and unobserved stochastic quantities are jointly modeled and the parameter uncertainty is fully acknowledged through the posterior predictive distribution. Several such rules have been recently considered and their asymptotic behavior has been characterized under the assumption that the observed features or variables used for building a classifier are conditionally independent given a simultaneous labeling of both the training samples and those from an unkn…
Tsinghua University（清华大学）；Chinese Academy of Sciences（中国科学院）；University of California, Berkeley（加州大学伯克利分校）；Joint Center for Global Change Studies（全球变化研究联合中心）
The objective of this paper is to evaluate the potential of Gaofen-2 (GF-2) high resolution multispectral sensor (MS) and panchromatic (PAN) imagery on water mapping. Difficulties of water mapping on high resolution data includes: 1) misclassification between water and shadows or other low-reflectance ground objects, which is mostly caused by the spectral similarity within the given band range; 2) small water bodies with size smaller than the spatial resolution of MS image. To solve the confusion between water and low-reflectance objects, the Landsat 8 time series with two shortwave infrared (…
State Key Laboratory of Remote Sensing Science, Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences（中国科学院遥感与数字地球研究所遥感科学国家重点实验室）；Ministry of Education Key Laboratory for Earth System Modeling, Center for Earth System Science, Tsinghua University（清华大学地球系统科学研究中心地球系统模拟教育部重点实验室）
There is a trend to acquire high accuracy land-cover maps using multi-source classification methods, most of which are based on data fusion, especially pixel- or feature-level fusions. A probabilistic graphical model (PGM) approach is proposed in this research for 30 m resolution land-cover mapping with multi-temporal Landsat and MODerate Resolution Imaging Spectroradiometer (MODIS) data. Independent classifiers were applied to two single-date Landsat 8 scenes and the MODIS time-series data, respectively, for probability estimation. A PGM was created for each pixel in Landsat 8 data. Condition…
Model selection and learning the structure of graphical models from the data sample constitutes an important field of probabilistic graphical model research, as in most of the situations the structure is unknown and has to be learnt from the given dataset. In this paper, we present a new forward model selection algorithm for graphical log-linear models. We use mutual conditional independence check to reduce the search space which also takes care of the evaluation of the joint effects and chances of missing important interactions are eliminated. We illustrate our algorithm with a real dataset e…
With the advent of so-called default Bayesian hypothesis tests, scientists in applied fields have gained access to a powerful and principled method for testing hypotheses. However, such default tests usually come with a compromise, requiring the analyst to accept a one-size-fits-all approach to hypothesis testing. Further, such tests may not have the flexibility to test problems the scientist really cares about. In this tutorial, I demonstrate a flexible approach to generalizing one specific default test (the JZS t-test; Rouder et al., 2009) that is becoming increasingly popular in the social …
We investigate probabilistic graphical models that allow for both cycles and latent variables. For this we introduce directed graphs with hyperedges (HEDGes), generalizing and combining both marginalized directed acyclic graphs (mDAGs) that can model latent (dependent) variables, and directed mixed graphs (DMGs) that can model cycles. We define and analyse several different Markov properties that relate the graphical structure of a HEDG with a probability distribution on a corresponding product space over the set of nodes, for example factorization properties, structural equations properties, …
Probabilistic graphical models are a powerful tool to represent real-word phenomena and to learn network structures starting from data. This paper applies graphical models in a new framework to study association rules driven by consumer choices in a network of museums. The network consists of the museums participating in the program of Abbonamento Musei Torino Piemonte, which is a yearly subscription managed by the Associazione Torino Città Capitale Europea. Consumers are card-holders, who are allowed to entry to all the museums in the network for one year. We employ graphical models to highli…
